States of matter
Intermolecular forces – forces of attraction and
repulsion between interacting particles (atoms and molecules). These are also
known as Vander Waals force of attraction. Types of Vander Waal forces:-
1)
Ion-dipole
forces: attractive forces between an ion and a dipole. E.g. NaCl + H2O.
2) Dispersion
forces or London forces: atoms or non-polar molecules are
electrically symmetrical and have no dipole moment. But a dipole may develop
momentarily even in such atoms and molecules. If the momentarily electronic
charge distribution in one of the atoms becomes unsymmetrical, this results in
the development of instantaneous dipole on the atom for very short interval of
time. This distorts the electron density of other atoms which are closer to it
and as a result the dipole is induced in other atoms. These are temporary
dipoles. E.g.: Noble gases, H2, etc.
3) Dipole-dipole
forces: present between the molecules possessing permanent dipoles.
E.g.: H2O, HCl.
4)
Dipole-Induced
dipole: between polar molecules having permanent dipoles and
molecules which are non-polar. Permanent dipole of polar molecules induces
dipole on the electrically neutral molecule by deforming its electronic clouds.
E.g.: Cl2 and H2O.
5)
Hydrogen
bond: requires (i) H-Atom, (ii) small size electronegative atom
(F, O, N). E.g.: water, ammonia.
Thermal Energy : It
is the measure of average kinetic energy of particles of the matter and their motion.
Order of intermolecular
force of attraction: Gas < liquid < solid.
Order of thermal energy: Gas > liquid > solid.
Gaseous State:
Only 11 elements exist as
gas under normal conditions: He, Ne, Ar, Kr, Xe, Rn, F, Cl, O, N, H.
They are highly compressible
and diffusible.
Parameters:
a) Volume: 1L=1 dm3=
1000cm3= 1000 ml.
b) Pressure : measured by
barometer ( atmospheric pressure) and manometer ( P of gas). 1 atm = 760mm =
760 torr = 1 bar = 101,325 Pa.
c) Temperature (oC,
K or F)
Gas laws:
1) Boyle’s law : At constant temperature, pressure of fixed mass of gas is inversely
proportional to volume. i.e P α 1/V
OR PV=Constant.
P1V1
= P2V2
Isotherm: Graph between P and V at constant temperature.
Significance
of Boyle’s law: The gases are compressible. The more it is pressed, the denser
it becomes. Therefore, at constant temperature, density of gas is directly
proportional to pressure. At altitudes, as atmospheric pressure is low, the air
is less dense. As a result, less oxygen is available for breathing. That is why
the mountaineers have to carry oxygen cylinders with them.
2) Charles’ law:
(given by Jacques Charles and extended by Joseph Gay Lussac) At constant Pressure, volume of a given
mass of a gas increases or decreases by 1/273.15 of its volume at 0oC
for every one degree centigrade rise or fall in temperature.
This implies that a gas at
-273.150C will have zero or no volume, i.e., it will cease to exist.
Absolute zero: The lowest hypothetical or
theoretical temperature of -273.15oC at which a gas is supposed to
have zero volume is called absolute zero.
Lord Kelvin suggested a new
scale of temperature starting with -273.150C as its zero. This scale
of temperature is known as Kelvin or
absolute scale of temperature. (273K to 373K)
Also, at constant
temperature for a fixed mass of gas, Volume α Temperature.
V/T = constant.
Isobar: Graph between V and T at constant Pressure.
Significance of Charles’
law: Air expands on heating and hence its density decreases. Thus hot air is
lighter than the atmosphere air and is used in filling hot air in the balloons
which rise up for meteorological observations.
3) Gay- Lussac’s law or Amonton’s law: At constant volume, Pressure of
a given mass of a gas increases or decreases by 1/273.15 of its pressure at 00C
for every centigrade rise or fall in temperature.
Also, at constant
temperature for a fixed mass of gas, Pressure α Temperature.
P/T = constant.
Isochore: Graph between P and T at constant Volume.
4) Avogadro’s law: According to it, equal volumes of all gas under the
same conditions of temperature and pressure contain equal number of molecules.
Volume α no. of moles
5) Ideal Gas: A gas that follows Boyle’s law, Charles’ law and
Amonton’s law strictly is called an ideal gas. Such a gas is hypothetical.
Ideal Gas Equation:
Boyle’s law: PV = Constant
at constant T and n
Charles’law: V/T = Constant
at constant P and n
Amonton’s law: P/T =
Constant at constant V and n
Avogadro’s law: V α n at
constant P and T.
PV/T = Constant i.e. PV
= nRT
Where R = Universal Gas Constant
= 8.314 J/K/mol = 0.0831 L atm/k/mol.
This is an equation of state. It
is a relation between four variables and it describes the state of any gas.
Combined gas law:
Units of R:
6) Dalton’s law of partial pressure: (given by John Dalton)
According to it, the total
pressure exerted by the mixture of non-reacting gases is equal to the sum of
the partial pressures of individual gases. In a mixture of gases, pressure
exerted by the individual gas is called partial pressure of a gas.
Ptotal = P1 + P2 + P3
+ …….. at constant temperature and volume
Pdry gas = Ptotal
– aqueous tension.
Aqueous tension = Pressure
exerted by saturated water vapours.
7) Relationship between density of a gas and its molar mass:
As PV = nRT and no. of moles
= given mass (w)
Molar
mass (M)
Kinetic molecular theory of gases:
(given by Bernoulli and then Clausius)
Postulates or assumptions-
a) Every gas is made up of
large number of molecules that are so small and so far apart that the actual
volume of molecules is negligible in comparison to the empty space between
them. They are considered as point masses. (This assumption explains
compressibility of gas).
b) There is no force of
attraction between particles of a gas at ordinary temperature and pressure. (It
explains that gases expand and occupy all the space available to them)
c) Particles of a gas are
always in constant and random motion. (Explains indefinite shape of gas)
d) Particles of gas move in
all possible directions in straight lines with different velocities due to which
they collide with each other as well as on the container.
e) Collisions of gas
molecules are perfectly elastic collision, i.e., the total energy of molecules before
and after the collision remain same.
f) At any particular time,
the molecules are moving with different velocities and possess different
kinetic energy. Average kinetic energy of gas molecules is directly
proportional to the absolute temperature of the gas.
Deviations from ideal gas behavior- (Real Gases)
Real gases are those gases
which do not obey ideal gas equation. They show deviations from ideal gas
behavior. The extent to which a real gas deviates from ideal gas behavior can
be conveniently studied in terms of a quantity ‘Z’ called as the compressibility factor which is the
ratio of product PV and nRT.
(i) For an ideal gas, PV = nRT i.e. Z = 1
(ii) For real gas, PV = nRT
Therefore, when Z<1, gas shows negative deviation i.e. gas
is more compressible than expected from ideal behavior.
When Z>1, gas shows positive deviation i.e. gas is less
compressible than expected from ideal behavior.
Extent of deviation depends
upon the nature of the gas.
Q Why do gases deviate from ideal behavior?
Causes: Two assumptions of
the kinetic theory do not hold good-
a) There is no force of
attraction between the molecules of gas.
b) Volume of molecule of gas
is negligibly small in comparison to the space occupied by the gas.
If assumption a) is correct,
the gas will never liquefy. If assumption b) is correct, pressure Vs volume
graph of real gas and ideal gas should coincide.
Equation of state for real gases - (Vander Waal’s equation)
For one mole of gas:
For n moles of gas:
Where a and b are Vander Waal’s
constants. Their values depend upon nature of gas.
Derivation- by modifying
ideal gas equation PV = nRT
(i) Correction for volume-
When the molecules are moving, their effective volume is four times the actual
volume i.e. 4v. Thus, the free volume available to the gas molecule for the
movement i.e. corrected volume = (V-b) for 1 mole or (V-nb) for n moles, where
b = 4v = excluded volume or co-volume.
(ii) Correction of pressure- A molecule lying within the vessel is
attracted equally by other molecules on all sides but a molecule near the wall
is attracted by the molecules inside. Corrected P = P + p
Where p α (density)2 and density α (n/V) for n moles or (1/V) for 1
mole.
Corrected P = P + an2/V2.
Therefore, Vander Waal’s equation: (P + an2/V2)
(V – nb) = nRT
Significance of Vander Waal’s constants:
(i) ‘a’ – It is a measure of
the magnitude of the attractive forces among the molecules of gas. Greater the
value of ‘a’, larger are the intermolecular forces of attraction.
(ii) ‘b’ – It is a measure
of effective size of gas molecules. It is equal to the four times the actual
volume of gas molecules. It is called excluded or co-volume.
Units of ‘a’ and ‘b’:
‘a’ : P = an2/V2 a = PV2/n2 = atm L2
mol-2
‘b’ : V = nb b = V/n = L/mol
Real gases obey ideal gas equation at- (i) low pressure, (ii)
high temperature
(as a/V2 and b
become negligible at these conditions)
Boyle temperature or boyle point:
The temperature at which a real gas obeys ideal gas law over an appreciable
range of pressure is called boyle temperature.
Also Z = Vreal /
Videal
Liquifaction of gases: First complete data
on P-V-T relations of a substance in both gaseous and liquid state was obtained
by Thomas Andrews on CO2. He plotted isotherms of CO2 at
various temperatures. Andrews noticed that at high temperature isotherms look
like that of an ideal gas and the gas cannot be liquefied even at very high
pressure.
Critical Temperature (Tc) –
The temperature above which a gas cannot be liquefied howsoever high pressure
may be applied on the gas. Volume of one mole of the gas at critical temperature
is called critical volume (Vc) and pressure at this temperature is
called critical pressure (Pc). For CO2, Tc =
31.10C or 30.980C.
Methods for gas liquefaction: a)
By increasing pressure, b) By decreasing temperature.
Importance
of Tc : Tc is a measure of strength of intermolecular
forces of attraction of that gas. Weaker are the intermolecular forces of
attraction, difficult it is to liquefy that gas and hence lower would be the Tc
of gas.
Vander
Waal’s constant ‘a’ is a measure of intermolecular forces of attraction.
Greater the value of ‘a’ is,
higher would be the value of Tc of that gas.
Liquid state - Various properties:
a) Vapour Pressure – It is the pressure exerted by the vapours on the
surface of liquid molecules when an equilibrium is established between liquid
phase and vapour phase. It is known as equilibrium or saturated vapour
pressure.
Boiling point – Temperature at which
vapour pressure of a liquid is equal to the external pressure.
Normal boiling point - at 1atm pressure and Standard boiling
point – at 1bar pressure. [as 1 bar < 1atm, therefore, normal boiling point
(1000C) > standard boiling point (99.60C) {1 atm =
1.03 bar}]
At high altitudes
atmospheric pressure is low, therefore, liquids boil at lower temperature at
high altitudes in comparison to that at sea level. Since, water boils at low
temperature on hills, pressure cooker is used for cooking food.
Factors affecting vapour pressure:
(i) Nature of liquid – If
intermolecular forces of attraction are weak, molecules can easily leave the
liquid and come into the vapour phase and exert more vapour pressure.
(ii) Temperature –
Temperature increases, vapour pressure increases.
b) Surface tension – Force acting at right angles to the surface along
one cm length of surface. Unit of γ = N/m. γ
= Force / length
The energy required to
increase the surface area of liquid by 1 unit is called surface energy. Unit = J / m2.
A molecule lying inside the
liquid is surrounded by other molecules and so is attracted by them equally in
all directions. Hence, net force acting by them equally in all directions.
Hence, net force acting on it is zero. While, a molecule at the surface is
attracted more by the molecules lying in the bulk of liquid than by the
molecules lying above it in the vapour phase. Thus, a molecule lying at the
surface experiences a net inward attraction. Thus, surface behaves as if it is
under tension. As a result, surface of liquid tends to contract to the smallest
possible area for a given volume of a liquid.
Surface tension tries to decrease the surface area of liquid
to minimum. The drops of liquid are spherical because for a given volume, a
sphere has minimum surface area.
Liquid tends to rise (or
fall) in the capillary because of surface tension. It is surface tension which
gives stretching property to the surface of liquid.
Cohesive forces – Attracting forces
existing between the molecules of same substance. E.g. – molecules of water.
Adhesive forces - Attracting forces
existing between the molecules of different substances. E.g. – molecules of
water and glass.
In case of water that wets
glass has concave or lower meniscus (curved surface of liquid) because adhesive
forces are stronger than cohesive forces while coloured liquids show upper
meniscus in glass tube because in these liquids, cohesive forces are stronger.
Factors affecting surface tension:
(i) Temperature –
Temperature increases, kinetic energy of molecules increases and intermolecular
forces decrease, so surface tension decreases.
(ii) Intermolecular forces
of attraction – increases, surface tension increases.
c) Viscosity – It is the measure of resistance to flow which arises
due to the internal friction between layers of fluid as they slip past one
another while liquid flows.
Laminar flow: Flow in which
there is regular gradation of velocity in passing from one layer to the
next.
F = η.A.dV/dx
where η = coefficient of
viscosity, F = Force of viscosity, A = area, dV/dx = velocity gradient.
η = It is the force of friction between the layers of liquid
when velocity gradient is unity and the area of contact is unit area.
Unit of η = Ns/m2 (in SI unit) = Poise (in cgs unit- named after
Jean Louise Poiseuille)
Factors affecting viscosity:
(i) Temperature –
Temperature increases, kinetic energy of molecules increases, liquid starts
flowing faster, viscosity decreases.
(ii) Intermolecular forces
of attraction – increases, viscosity increases.
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